What is the maximum number of parallel tangents a circle can have on a diameter?

Answer

To determine the maximum number of parallel tangents a circle can have on a diameter, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Tangents**: A tangent to a circle is a straight line that touches the circle at exactly one point. It does not cross the circle.

2. **Identifying the Diameter**: Consider a circle with a diameter. Let's denote the endpoints of the diameter as points A and B.

3. **Drawing the Diameter**: Draw a horizontal line segment AB, which represents the diameter of the circle.

4. **Positioning the Circle**: Place the circle such that its center is at the midpoint of the diameter AB. The circle will extend above and below this diameter.

5. **Drawing Parallel Tangents**: For any given point on the diameter, there can be a tangent line that touches the circle at that point.

6. **Maximum Parallel Tangents**: Since the diameter is a straight line, we can draw two parallel tangents to the circle at the endpoints of the diameter (points A and B). These tangents will be horizontal lines that run parallel to the diameter.

7. **Conclusion**: Therefore, the maximum number of parallel tangents that can be drawn on the diameter of a circle is **2**.

### Final Answer:
The maximum number of parallel tangents a circle can have on a diameter is **2**.

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